help 1.the pressure wave that travels along the inside of an organ pipe is given

Question

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1.the pressure wave that travels along the inside of an organ pipe is given in terms of distance and time by the following function p ( x, t ) = ( 1.0 atm ) sin [ ( 6.0 rad / m ) x - ( 4.0 rad / s ) t ]. what is the pressure amplitude of the wave? what is the wave number of the wave? what is the frequency of the wave? what is the speed of the wave? what is the corresponding spatial displacement, s ( x, t ), from equilibrium for the pressure wave, assuming the maximum displacement is 2.0 cm?
2. two identical guitar strings under 200 N of tension produce sound with frequencies of 290Hz. if the tension in one string drops to 196N, what will be the frequency of beats when two strings are plucked at the same time?
3. a bicyclist is moving toward a sheer wall while holding a tuning fork rated at 484 Hz. if the bicyclist detects a beat frequency of 6Hz (between the waves coming directly from the tuning fork and the echo waves coming from the sheer wall), calculate the speed of the bicycle. assume the speed of sound is 3.43 m/s.

Explanation / Answer

Here ,

p = 1 * sin(6 x - 4 t ) atm

as y = A * sin(k*x - w *t )

a)

pressure ampitude = A

pressure ampitude = 1 atm

b)

Now , wave number , k = 6 rad/m

c)

frequency = w/2pi

frequency = 4/2pi

frequency = 0.637 Hz

d)

speed of wave = w/k

speed of wave = 4/6

speed of wave = 0.67 m/s

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