Question

The ripples in a certain groove 11.1 cm from the center of a 33-rpm phonograph record have a wavelength of 2.60 mm .

What will be the frequency of the sound emitted?

Answer 1

At 11.1 cm from the center of the record, the radius of one groove is r = 11.1 cm.

So, the circumference of one groove L = 2 x r = 2 x 3.14 x 11.1 cm = 69.708 cm.

Since the record is turning at 33 rpm, the needle on the record is travelling through the groove at a linear speed of v = 33 x L / min = ( 33 x 69.708 / 60 ) cm / s = 38.34 cm / s.

The ripples have a wavelength of = 2.6 mm = 0.26 cm.

So, the frequency of the sound emitted from the phonograph record is :

f = v / = ( 38.34 cm / s ) / 0.26 cm = 147.46 Hz.