Question

A sound wave caused by a piano has a frequency of 678 Hz, and the speed in air is 330 m/s.

(a) What is the wavelength of this wave?

(b) At any given point in space, how long does it take for the air to go from maximally compressed to maximally expanded?

(c) For two points 72.5 cm apart, what is the phase difference of the wave between these points?

Answer 1

Solution) f = 678 Hz

V = 330 m/s

(a) Wavelength , Lambda= ?

V = f(Lambda)

Lambda = (V)/(f)

Lambda = (330)/(678)

Lambda = 0.486 m

Therefore , wavelength Lambda = 0.486 m

(b) time , T' = ?

T = 1/f

T = 1/(678)

T = 0.00147 s

Maximally compressed to maximally expanded occurs at

T' = (T/4)

T' = (0.00147/4)

T' = 0.00036 s

T' = 0.3675×10^(-3) s

T' = 0.3675 ms

(c) Phase difference = ?

Phase difference = (2(pi)/(Lambda))(path difference)

Path difference = 72.5 cm = 0.725 m

Phase difference = (2(pi)/(0.486))(0.725)

Phase difference = 9.37 radians