The equation of a standing wave, produced on a string fixed at both ends, is y = (0.4 cm) sin[(0.314 cm−1)x] cos[(600 π s−1)t]
What could be the smallest length of the string?
10 cm
we get from the wave equation that ω = 600 π
⇒ f = ω2π = 300 Hz
Also k = 0.314
⇒ 2πλ = 0.314
λ = 2π0.314
λ = 20 cm
velocity,v= fλ = 300 × 20
= 6000 cm s−1
And as we know f = nv2L
L = nv2f = n × 60002 × 300
L = 10 n
The least value for n = 1
so Lmin = 10 cm