Question

A cord 80 cm long is stretched by a load of 8 kgf. The mass per unit length of the
cord is 4 x 10-5 kg m-!. Find:
iSpeed of the transverse wave in the cord, and
(ii) Fundamental frequency of vibration.​

Answer 1

Explanation:

Given A cord 80 cm long is stretched by a load of 8 kgf. The mass per unit length of the  cord is 4 x 10-5 kg m-!. Find:  (i) Speed of the transverse wave in the cord, and  (ii) Fundamental frequency of vibration.​

• We know that velocity v = √T / m
• T = F = 8 x 9.8
• m = 4 x 10^-5
• Now v = √8 x 9.8 / 4 x 10^-5
• Or v = √19.6 x 10^5  
• Or v = 1400 m/s is the speed of transverse wave.
• Now frequency ν = 1 / 2L √T / m
•                            = 1 / 2 x 0.8 √1400
•                          =  14,000 / 2 x 8
•                             = 7000 / 8
•                            = 875 hertz

Fundamental frequency of vibration is 875 hertz.