# Physic Questions about Sound and Dopplers Effect

Question 1: Particles approximately 3.0 X 10-2 cm in diameter are to be scrubbed loose from machine parts in an aqueous ultrasonic cleaning bath. Above what frequency should the bath be operated to produce wavelengths of this size and smaller? Helpful tip. The speed of sound (s) is equal to the frequency (f) times the wavelength (lambda). In order for the particles to be removed by the sound wave, the wavelength must be equal to the size of the particles. Use the aforementioned equation for the speed of sound (s = f * lambda) to solve for the frequency.

Question 2: Brass is an alloy of copper and zinc. Does the addition of zinc to copper cause an increase or decrease in the speed of sound in brass rods compared to copper rods? Explain.

Question 3: The size of your eardrum (the tympanum) partially determines the upper frequency limit of your audible region, usually between 16,000 Hz and 20,000 Hz. If the wavelength is about twice the diameter of the eardrum and the air temperature is 20 degrees Celsius, how wide is your eardrum? Is your answer reasonable? Helpful tip. Using the speed of sound equation [331 m/s + (0.6)Tc = f * lambda since the speed of sound is temperature dependent in this case], solve this equation for the wavelength (lambda) at both extremes. Once you have obtained the wavelength for each case, divide the result by 2 to obtain the approximate size of the eardrum.

Question 4: Sound propagating through air at 30 degrees Celsius passes through a vertical cold front into air that is 4.0 degrees Celsius. If the sound has a frequency of 2400 Hz, by what percentage does its wavelength change in crossing the boundary? Helpful Tip. Calculate the wavelength of the sound at 30 degrees Celsius [use 331 m/s + (0.6)Tc = f * lambda to and solve for the wavelength]. Next, calculate the wavelength at 4 degrees Celsius using the same equation as in the first case. Take the second wavelength you obtained and divide it by the first. Multiply the result by 100 to obtain the percentage. Finally, subtract this result from 100% to obtain the percent decrease.

Question 5: Explain the physics of the generation of sound for a musical instrument of your choice.

Question 6: How fast in kilometers per hour, must a sound source be moving toward you to make the observed frequency 5.0% greater than that observed when the source is stationary with respect to you? (Assume that the speed of sound is 340 m/s.) Helpful Tip. Use equation 9.11 on page 316 of the text. Substitute 1.05fs for fo in the equation. This will allow you to later cancel them out of the equation. Finally, solve for vs.

Question 7: Two point-source loudspeakers are a certain distance apart, and a person stands 12.0 m in front of one of them on a line perpendicular to the baseline of the speakers. If the speakers emit identical 1000.0-Hz tones, what is their minimum nonzero separation so that the observer hears little or no sound? (Take the speed to be exactly 340 m/s.) Helpful Tip. First, calculate the wavelength (use s = f * lambda). Next, use equation 9.7 (deltaL = lambda/2 where deltaL = L1 - L2). Let the value of L1 = 12m. That would make the value of L2 = d - 12 m (i.e. the total distance minus 12 m). put it all together and solve for "d."

Question 8: Bats emit sounds of frequencies around 35.0 kHz and use echolocation to find their prey. If a bat is moving at the speed of 12.0 m/s toward an insect at an air temperature of 20.0 degrees Celsius, (assume the insect and air are still)

(a) What frequency is heard by the insect?

(b) What frequency is heard by the bat from the reflected sound?

(c) Would the speed of the bat affect the answers?

Helpful Tip. First, find the speed of sound at the specified temperature [use 331 m/s + (0.6)Tc]. Next, use equation 9.11 to find fo (note: vs = 12 m/s).

Question 9: A tuning fork with a frequency of 440 Hz is held above a resonance tube that is partially filled with water. Assuming that the speed of sound in air is 342 m/s, for what three smallest heights of the air column will resonance occur? Where will the nodes and antinodes occur? (Hint: For resonance to occur, the frequency of the tuning fork must match that of the tube.) Helpful Tip. Using equation 9.18, and taking f1 to be 440 Hz, calculate L for m = 1, 3, and 5.

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#### Solution Preview

Question 1: Answer: We know that the speed of sound can be written as v = fλ where v is the speed of sound. To remove the particles from the machine parts, we must use a wave whose wavelength is equal to the size of the particle. Hence the wavelength must be equal to the diameter of the particles. Now using this we can find the frequency as f = v / lambda;. Here the velocity of the ultrasonic waves must be given to solve this problem. But this velocity in an aqueous solution is well known as 1200 ms-1. Now it can be given by frequency

Question 2: The speed of sound depends on the elastic modulus(E) of the given metal as where d is the density of the material. Here the zinc has less elasticity when compared to the copper. Hence the mixture of zn and cu will reduce the effective elasticity of the alloy. Now the effective speed of the mixture will reduce.

Question 3: Here the value of the speed of sound at 0 ...

#### Solution Summary

This solution is comprised of a detailed, step wise response which solves each of the nine physics-based problems, with an explanation and the required calculations.

Physics Problems: Displacement, Velocity, Acceleration, Frequency, Equilibrium Position, Sound Intensity

32. A 0.50-kg mass oscillates in simple harmonic motion on a spring with a spring constant of 200 N/m. What are:

a) The period?

b) The frequency of the oscillation?

48. The equation of motion of a particle in vertical SHM is given by y = (10 cm) sin 0.50t. What are the particle's:

a) Displacement?

b) Velocity?

c) Acceleration at t = 1.0 s?

70. A sonar generator on a submarine produces periodic ultrasonic waves at a frequency of 2.50 MHz. The wave-length of the waves in seawater is 4.80 x 10^-4 m. When the generator is directed downward, an echo reflected from the ocean floor is received 10.0 s later. How deep is the ocean at this point? (Assume the wavelength is constant at all depths.)

90. The fundamental frequency of a stretched string is 100 Hz. What are the frequencies of:

a) The second harmonic?

b) The third harmonic?

100. A 0.10-kg mass suspended on a spring is pulled to 8.0 cm below its equilibrium position and released. When the mass passes through the equilibrium position, it has a speed of 0.40 m/s. What is the speed of the mass when it is 4.0 cm from the equilibrium position?

16. Particles approximately 3.0 x 10^-2 cm in diameter are to be scrubbed loose from machine parts in an aqueous ultrasonic cleaning bath. Above what frequency should the bath be operated to produce wavelengths of this size and smaller?

48. A person standing 4.0 m from a wall shouts such that the sound strikes the wall with an intensity of 2.5 x 10^-4 W/m^2. Assuming that the wall absorbs 20% of the incident energy and reflects the rest, what is the sound intensity level just before and after the sound is reflected?

50. A 1000-Hz tone from a loudspeaker has an intensity level of 100 dB at a distance of 2.5 m. If the speaker is assumed to be a point source, how far from the speaker will the sound have intensity levels:

(a) Of 60 dB?

(b) Barely high enough to be heard?

64. What is the frequency heard by a person driving 50 km/h directly toward a factory whistle (f = 800 Hz) if the air temperature is 0 degrees C?

74. Bats emit sounds of frequencies around 35.0 kHz and use echolocation to find their prey. If a bat is moving with a speed of 12.0 m/s toward an insect at an air temperature of 20.0 C, :

a) What frequency is heard by the insect?

b) What frequency is heard by the bat from the reflected sound?

c) Would the speed of the bat affect the answers?