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Chapter 2: Q40E (page 540)
Two guitarists attempt to play the same note of wavelength at the same time, but one of the instruments is slightly out of tune and plays a note of wavelength instead. What is the frequency of the beats these musicians hear when they play together?
The beats have the frequency .
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Longitudinal Waves on a Spring. A long spring such as a is often used to demonstrate longitudinal waves. (a) Show that if a spring that obeys Hooke’s law has mass m, length L, and force constant k′, the speed of longitudinal waves on the spring is
(see Section 16.2). (b) Evaluate v for a spring with m = 0.250 kg, L = 2.00 m, and k′ = 1.50 N/m.
BIO Audible Sound. Provided the amplitude is sufficiently great, the human ear can respond to longitudinal waves over a range of frequencies from about 20.0 Hz to about 20.0 kHz . (a) If you were to mark the beginning of each complete wave pattern with a red dot for the long-wavelength sound and a blue dot for the short-wavelength sound, how far apart would the red dots be, and how far apart would the blue dots be? (b) In reality would adjacent dots in each set be far enough apart for you to easily measure their separation with a meter stick? (c) Suppose you repeated part (a) in water, where sound travels at 1480 m/s . How far apart would the dots be in each set? Could you readily measure their separation with a meter stick?
A loud factory machine produces sound having a displacement amplitude of 1.00 μ-m, but the frequency of this sound can be adjusted. In order to prevent ear damage to the workers, the maxi mum pressure amplitude of the sound waves is limited to 10.0 Pa. Under the conditions of this factory, the bulk modulus of air is 1.42 x 105 Pa. What is the highest-frequency sound to which this machine can be adjusted without exceeding the prescribed limit? Is this frequency audible to the workers?
A bat flies toward a wall, emitting a steady sound of frequency 1.70 kHz. This bat hears its own sound plus the sound reflected by the wall. How fast should the bat fly in order to hear a beat frequency of 8.00 Hz?
Two loudspeakers, A and B (see Fig. E16.35), are driven by the same amplifier and emit sinusoidal waves in phase. Speaker B is 2.00 m to the right of speaker A. The frequency of the sound waves produced by the loudspeakers is 206 Hz. Consider a point P between the speakers and along the line connecting them, a distance x to the right of A. Both speakers emit sound waves that travel directly from the speaker to point P. For what values of x will (a) destructive interference occur at P; (b) constructive interference occur at P? (c) Interference effects like those in parts (a) and (b) are almost never a factor in listening to home stereo equipment. Why not?
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