Question

20. A string (length 1 m, tension 100 N) is clamped at both ends. The string resonates with transverse waves at the fundamental frequency of 250 Hz. What is the mass of the string? 21. A speaker generates sound waves isotropically. The total sonic power produced by the speaker is 1 W. What is the sound intensity level (in decibels) at a distance of 100 m from the speaker?

Answer 1

20.

L = length of string = 1 m

T = 100 N

fundamental frequency is given by:

f1 = v/2L

v = f1*2*L

v = 250*2*1 = 500 m/sec

Now we know that

v = sqrt (T/d)

d = linear density = m/L

v = sqrt (T*L/m)

m = T*L/v^2

m = 100*1/500^2 = 0.0004 kg

mass = 0.4 gm