A 660 Hz tuning fork sets up vibration in a string clamped at both ends. The wave speed for a transverse wave on this string is `1220 m s^-1` and the string vibrates in three loops. (a) Find the length of the string. (b) If the maximum amplitude of a particle is 0.5 cm, write a suitable equation describing the motion.

A 660 Hz tuning fork sets up vibration in a string clamped at both end

1.	A 660 Hz tuning fork sets up vibration in a string clamped at both ends. The wave speed for a transverse wave on this string is `1220 m s^-1` and the string vibrates in three loops. (a) Find the length of the string. (b) If the maximum amplitude of a particle is 0.5 cm, write a suitable equation describing the motion.
Answer» Correct Answer - a) 50cm b) `cos(0.06picm^-1)sin((1320pis^-1)t)` Frequency of the tunning fork, `f=660Hz` Wave speed `v=220m/s` `rarr `lamda`=V/f=220/660=1/3m` No.of loops = 3 a. So, L.`f=(3/2)v` `rarr L.660=(3/2)xx220` ` L=1/2m=50cm` b. the equation of resultant statioN/Ary wave is given by, `y=2Acos((2pix)/lamda)sin((2pivt)/lamda)` `rarr y=(0.5)cos((2pix)/(1/3m))sin((2pixx220xxt)/lamda)` `rarr y=(0.5cm)` `cos(6pixm^-1)sin(1320pis^-1t)` `rarr y=(0.5cm)` `cos(0.06picm^-1)sin(1320pis^-1t)`

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