A wire stretched between two rigid supports vibrates in its fundamental mode with a frequency of 45 Hz. The mass of the wire is 3.5 x 10⁻² kg and its linear mass density is 4.0 x 10⁻² kg m⁻¹. What is the speed of a transverse wave on the string?
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given,
mass of wire, m = 3.5 × 10^-2 kg
linear mass density , u = 4 × 10^-2 kg
so, length of wire , l = m/u = 3.5/4 = 0.875m
frequency of fundamental mode , f = 45Hz
for wire stretched between two rigid supports,
fundamental mode is given by,
l = λ/2 => λ = 2l = 2 × 0.875 = 1.75 m
now, use formula, v = λf , to find speed of wave
so, v = 1.75 × 45 = 78.75 m/s
hence speed of the transverse wave on the string is 78.75 m/s
mass of wire, m = 3.5 × 10^-2 kg
linear mass density , u = 4 × 10^-2 kg
so, length of wire , l = m/u = 3.5/4 = 0.875m
frequency of fundamental mode , f = 45Hz
for wire stretched between two rigid supports,
fundamental mode is given by,
l = λ/2 => λ = 2l = 2 × 0.875 = 1.75 m
now, use formula, v = λf , to find speed of wave
so, v = 1.75 × 45 = 78.75 m/s
hence speed of the transverse wave on the string is 78.75 m/s
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