Q.
The transverse displacement of a string fixed at both ends is given by y=0.06sin(32πx)cos(100πt) where x and y are in metres and t is in seconds. The length of the string is 1.5m and its mass is 3.0×10−2kg. What is the tension in the string?
On comparing y=0.06sin(32πx)cos(100πt)
with y=Asin(kx)cos(ωt), we get k=32π
and ω=100πrad/s
Velocity of the wave, v=kω=(32πrad/m)(100πrad/s)=150m/s...(i)
Here, L=1.5m,m=3.0×10−2kg
Mass per unit length of the string, μ=Lm=1.5m3.0×10−2kg=2×10−2kg/m
Velocity of a transverse wave on a stretched string is v=μT...(ii)
where T is the tension in the string and μ is the mass per unit length of the string.
From (i) and (ii), we get 150=2×10−2T or T=(150)2×2×10−2N=450N