Potentially useful equations: v = Lambda f = Lambda/T traveling wave: y(x,t) = A

Question

Potentially useful equations: v = Lambda f = Lambda/T traveling wave: y(x,t) = A sin(2pit/T - 2pix/Lambda + phi) Two-slit/diffraction grating interference maxima: d sintheta = nLambda A sound wave, which is a pressure wave in air, is produced by a tuning fork. The wave is described by the following equation: P(x,t) - A sin(2pit/T - 2pix/Lambda) where A = 2 Pa (where the unit of pressure is 1 Pa = 1 N/m^2). The period of the wave is 0.002 s. If the speed of sound in air is 330 m/s, what is the wavelength of the wave described by the above equation? Show your work (the equations) leading to your answer. The speed of sound in air increases slightly with temperature. If the temperature increases and the speed of sound goes from 330 m/s to 340 m/s, what happens to the frequency and wavelength of the sound wave from the tuning fork? Do they increase, decrease, or stay the same? Explain in one or two brief sentences. Given the graph below of a sound wave as a function of time, if the speed of sound is 330 m/s, estimate the frequency of the sound in Hz. (Remember that that 1 msec = 1/1000 sec.)

Explanation / Answer

1)

a) v = 330 m/s

T = 0.002

we know, frequency, f = 1/T = 1/0.002 = 500 hz

apply, v = lamda*f

==> lamda = v/f

= 330/500

= 0.66 m

b) frequency remains same.

we have, v = lamda*f

so, when v increases lamda also increases.

2)

from the graph, Time period, T = 2.5 ms = 2.5*10^-5 s

frequency, f = 1/T

= 1/(2.5*10^-3)

= 400 Hz

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