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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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Interference of Triangular Pulses. Two triangular wave pulses are traveling toward each other on a stretched string as shown in Fig. E15.32. Each pulse is identical to the other and travels at \(2.00\;{{{\rm{cm}}} \mathord{\left/ {\vphantom {{{\rm{cm}}} {\rm{s}}}} \right. \\} {\rm{s}}}\). The leading edges of the pulses are \(1.00\;{\rm{cm}}\) apart at \(t = 0\). Sketch the shape of the string at \(t = 0.250\;{\rm{s}}\), \(t = 0.500\;{\rm{s}}\), \(t = 0.750\;{\rm{s}}\), \(t = 1.000\;{\rm{s}}\), and \(t = 1.250\;{\rm{s}}\)
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?
A car alarm is emitting sound waves of frequency 520 Hz. You are on a motorcycle, traveling directly away from the parked car. How fast must you be traveling if you detect a frequency of 490 Hz?
Which of the following wave functions satisfies the wave equation, Eq. (15.12)? (a)\(y\left( {x,t} \right) = Acos\left( {kx + \omega t} \right)\) ; (b)\(y\left( {x,t} \right) = Asin\left( {kx + \omega t} \right)\) ; (c) \(y\left( {x,t} \right) = A\left( {coskx + cos\omega t} \right)\) (d) For the wave of part (b), write the equations for the transverse velocity and transverse acceleration of a particle at point x.
Question:What must be the stress (F/A) in a stretched wire of a material whose Young鈥檚 modulus is Yfor the speed of longitudinal waves to equal 30 times the speed of transverse waves?
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