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# Resonance

Acoustic resonance is the tendency of an acoustic system to absorb more energy when it is forced or driven at a frequency that is the same as one of its own natural frequencies of vibrations. Acoustic resonance is sometimes used to narrow mechanical resonance to the frequency range of human hearing. Since acoustics is defined in general terms concerning vibrational waves in matter, acoustic resonance can occur at frequencies outside the range of human hearing.

An acoustically resonant object usually has more than one resonance frequency. This is especially true at harmonics of the strongest resonance. The object will easily vibrate at these frequencies and vibrate less strongly at other frequencies. It can pick out its resonance frequency from a complex excitation such as an impulse or a wideband noise excitation; it is filtering out all frequencies other than its resonance.

Acoustical resonance is important for instrument builders. Most instruments used resonators, such as, the strings and body of a guitar, the length of tube in a flute, and the shape of a drum membrane. It is also important in hearing.

### Equation of motion, functions

A simple harmonic oscillator, of mass m and natural frequency w_0, experiences an oscillating driving force f(t)=m a cos(wt). Therefore, its equation of motion is d^2x/dt^2 + w^2_0x = acos(wt) where x is the position. Given that at t=0 we have x=dx/dt=0, find the function x(t). Use BOTH with variation of the parameters

### Calculate Impedance, Resonance Frequency; Draw Phasor Diagram

See attached file for proper format. 5a1.1. Calculate the impedance (XR) of R = 100 at f = 6 hz, 60 hz, and 600 hz. 5a1.2. Calculate the impedance (XC) of C = 100 F at f = 6 hz, 60 hz, and 600 hz. 5a1.3. Calculate the impedance (XL) of L = 100 mH at f = 6 hz, 60 hz, and 600 hz. 5a2.1. Draw a phasor diagra

### Force, Transverse Traveling and Natural Frenquency of a System

4. A 70 kg ancient statue lies at the bottom of the sea (fresh water). Its volume is 3.0*10^4 (cm)^3. a) How much force is required to lift it up at constant velocity through the water? (A force diagram would prove helpful in this problem). b) If the statue was in salt water instead of fresh water, would the force required to

### Frequency of sound, siren intensity, guitar string, wavelength

1. Suppose you place a speaker in front the open end of a tube which is closed at the other end, and vary the frequency of a pure sound (sine wave) produced by the speaker. You find that there are resonances at 300 Hz and 500 Hz, among many others. (A) resonance is a frequency at which the sound in the tube is very loud becau

### Tunning Fork and frequency

A tuning fork of frequency 550 Hz is placed near the top of the pipe shown in the Figure. The water level is lowered so that the length L slowly increases from an initial value of 20.0 cm. Determine the next two values of L that correspond to resonant modes. (Assume that the speed of sound in air is 343 m/s.) 1 m (shorter lengt

### Evaluating Standing Waves

1. For a particular tube there are six harmonic frequencies below 1000 Hz. Four of these are 300Hz, 600Hz, 750Hz, and 900Hz. You can see that one end of the tube is open, but you can not see the other end. Is it open or closed? Explain your answer. 2. In the tube described above, what two frequencies are missing? 3. When

### Harmonic Frequencies of a Pipe

1. Find a formula for the harmonic frequencies (fn) for a pipe open at only one end based on v=f*lamda and the formula we got for the harmonic wavelengths 2. For a pipe of length 0.40m, find the first five harmonic wavelengths and frequencies. 3. What length pipe is needed to play an A note (440Hz) in the second harmonic?

### Standing waves on stretched string and resonance.

Please do questions 1-5. Going through this lab, please see data table in second attachment, stringlab2.doc, when tried to solve for V th and the rest everything went wrong. V th never even was close to V average. This is throwing everything off. All data is assumed to be correct, but again V th is off. If cannot read here

### Driven Oscillations and Dampness

Show that , if a driven oscillator is only lightly damped and driven near resonance, the Q of the system is: Q = 2*Pi {(Total Energy)/(Energy loss during one period)} where Q = Wr/2B Wr = resonance (angular frequency) B = damping parameter

### Q-factor and resonant frequency

The Q-factor of a resonance circuit is defined as the ratio of the voltage across the capacitor (or inductor) to the voltage across the resistor, at resonance. The larger the Q-factor, the sharper the resonance curve will be and the sharper the tuning. Show that the Q-factor is given by the equation: (see attachment). At resonan

### Impedance and Current in an RLC Circuit at Resonance

What is the impedance of a series RLC circuit at resonance? What is the current in the circuit at resonance?

### Resonating Spring Constants

A 1.15 kg mass is suspended from a spring with a spring constant of 169.0 N/m. The spring is attached to a rod which oscillates vertically at a frequency f. For what value of the frequency f will the system resonate?

### Standing waves: Violin String Resonating with concert.

A violin string has a length of 0.350 m and is tuned to concert A, with frequency of A = 440 Hz. Where must the violinist place her finger to play F sharp, with frequency of f sharp = 740 Hz? If this position is to remain correct to half the width of a finger (that is, to within 0.600 cm), what is the maximum allowable perce

### Calculating capacitance and amplitude of a voltage

An L-R-C series circuit consists of a source with voltage amplitude 120V and angular frequency 50.0 rad/s, a resistor with R = 400 ohms, an inductor with L = 9.00H and a capacitor with capacitance C. a) For what value of C will the current amplitude in the circuit be a maximum? b) When C has the value calculated in part (a),

### Finding speed of transverse waves on a guitar string

The D note (at a frequency of 588 ) from a trumpet causes a guitar string to vibrate in its second overtone with large amplitude. The vibrating portion of the guitar string has a length of 64.0 . What is the speed of transverse waves on the guitar string? The way I've been trying to accomplish this problem is by saying tat

### Spring System Problem

1. A 2 kg block is attached to a spring and placed on a horizontal smooth surface. A horizontal force of 20 N is required to hold the block at rest when it is pulled 0.2 m from its equilibrium position. The block is released from its rest from this point, and is subsequently undergoes simple harmonic motion. Find a) the sprin

### RLC circuit : Resonance

An RLC circuit has a capacitance of 0.43 microF. (a) What inductance will produce a resonance frequency of 95 mHz? (b) It is desired that the impedance at resonance be 1/2 the impedance at 11 kHz. What value of R should be used to obtain this result?"

### Nine review problems: Force, energy, motion, frequency, amplitude, harmonic motion, oscillation, speed, tuning fork, beat frequency

See attachment for proper format. 1. An archer pulls his bow string back 0.4 m by exerting a force on the string that increases uniformly from zero to 230 N. What is the equivalent force constant of the bow? How much work does the archer do in pulling the bow? 2. A ball dropped from a height of h makes a perfectly elasti

### Sound - Resonant Frequency and the Missing Fundamental

Problem 6. Assume that the outer ear canal is a cylincrical pipe 3 cm long, closed at one end by the eardum. Calculate the resonant frequency (fundamental, v1) of this pipe. Our hearing should be especially sensitive for frequencies near this resonance. Problem 7. A "tonic" chord in the musical key of A-major consists of tone

### Evaluation of a RLC Circuit

Hi. Can someone please walk me through how to do the following problem? Question: A radio tuning circuit contains an RLC circuit with R=5.0 ohms and L=2.8 micro-H. (a) What capacitance is needed to produce a resonance frequency of 95 MHz? (b) If the capacitance is increased above the value found in part (a), will the imped

### Finding resonance wavelength and frequencies

Assume L=2m, V=340 m/s Find the resonance wavelength and frequencies.