7 Th the figure above a string is firmly attached at both en

7. Th the figure above, a string is firmly attached at both ends. When a frequency of 60 Hz is applied, the string vibrates in the standing wave pattern shown. Assume the tension in the string and its mass per unit length do not change. Which of the following frequencies could NOT also produce a standing wave pattern in the string? (A) 30 Hz 40 Hz Hz (D) 180 Hz

Solution

Answer is 30 Hz

The Given figure is 3^rd harmonic with frequency 60 Hz ,so fundmental frequency

f₃=3f =60

f=20 Hz

Therefore the other possible standing waves should be multiples of 20.so in given options 40 Hz,80 Hz and 180 Hz are other possible standing wave .

The frequency than could not produce a standing wave pattern in the string is 30 Hz