# Sound Waves

1. Imagine two symmetrical pulses that are identical in every way, except tht one is inverted. These pulses are moving toward each other on a rope in opposite directions. What happens to the energy of the rope at the instant of complete cancellation?

2. In the real world, a pulse sent down a very long, taut rope diminishes in amplitude and ultimately vanishes. Describe what's happening in terms of Conservation of Energy.

Multiple choice:

1. A periodic wave passes an observer, who records tht there is a time of .5 s between crests. (a) the frequency is .5 Hz (b) the speed is .5 m/s (c) the wavelength is .5 m (d) the period is .5 s (e) none of these. Explain your choice.

2. For a harmonic wave of a certain type in a given medium, doubling the frequency has the effect of: (a) halving the speed (b) halving the wavelength (c) doubling the amplitude (d) doubling the period (e) none of these. Explain your answer.

3. Quite generally, doubling the amplitude of a wave: (a) doubles the frequency (b) halves the period (c) quadurpled the energy (d) doubles the speed (e) none of these. Explain your choice.

Problem

1. A long metal rod is stuck by a vibrating hammer in such a way that a compression wave with a wavelength of 4.3 m travels down its length at a speed of 3.5 km/s. What was the frequency of the vibration?

2. Imagine a sinusoidal presssure wave for which the distance between successive maxima is 2.25 m. If exactly 10 such peaks pass a microphone each 1.00 s, what is the speed of the wave?

3. A person standing at one side of a playing field on a cold winter night emits a brief yell. The short acoustical wavetrain returns 1.00 s later as an echo having "bounced off" a distant dormitory. Approximately how far away was the building?

4. A low-frequency loudspeaker is called a woofer. At what frequency will a tone have a wavelength equal to the diameter of a 15-inch woofer? Take the speed of sound to be 344 m/s.

5. The speed of sound in ether (25 deg C, 1 atm) is 976 m/s. What is the wavelength in ether produced by a tuning fork oscillating at 1000 Hz?

6. Suppose that a tuning fork in air, where the speed of sound is 343 m/s, produces a tone having a wavelength of 0.7795 m. The fork is immersed in acetone and then tapped. How long a wave will be created in the liquid given the acetone (20 deg C, 1 atm) supports sound waves tht travel at 1203 m/s.

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#### Solution Preview

QUESTIONS:

(1) It appears as if, the energy should be zero but this is not the case, the energy contained in a wave, like anything else, has two parts, potential that is usually proportional to expansion (elongation, compressing, or else depending on your wave type) SQUARED, and a kinetic part proportinal to time derivative of expansion SQUARED (something like velocity of the points on the wave squared). Now at the point of cancellation, the two waves have zero overall potential energy, but their particles are still moving, and in fact they will be at their maximum kinetic energy, because the total energy will be conserved.

(2) In the real world energy is not conserved because of friction, that can have many forms, ...

#### Solution Summary

Sound Waves are examined in a variety of questions. The terms of conservation of energy is determined.