Waves travel along a taut string driven by a 125Hz oscillato

Waves travel along a taut string driven by a 125Hz oscillator at one end. If the waves have a velocity of 40m/s, what is the wavelength? If the string is 3m long with a mass of 5.4g, what is the tension in the string? If I increase string tension, does the wave speed increase, decrease, or no change? If I increase oscillator frequency, does the wave speed increase, decrease, or no change?If I increase string mass without changing length, does the wave speed increase, decrease, or no change?

Solution

Here,

frequency = 125 Hz

speed of wave , v = 40 m/s

wavelength = speed of wave/frequency

wavelength = 40/125

wavelength = 0.32 m

let the tension in the string is T

speed of wave = sqrt(T/(m/L))

125 = sqrt(T/(0.0054/3))

solving for T

T = 28.12 N

the tension in the string is 28.12 N

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when the string tension increases , the wave speed will increase

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wave speed is independent of frequency , the wave speed will be same if we change frequency.

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if string mass is increased , wave speed will decrease