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66. A string of length L consists of two sections. The left half has mass per unit length µ= µ,12, while the right has a mass per unit length u' = 3µ = 3µ, / 2µ . Tension in the string is T. Notice from the data given that this string has the same total mass as a uniform string of length L and mass per unit length µ̟. (a) Find the speeds v and v' at which transverse pulses travel in the two sections. Express the speeds in terms of T, and u,, and also as multiples of the speed v, = (T,/ µ̟)"² . (b) Find the time interval required for a pulse to travel from one end of the string to the

66. A string of length L consists of two sections. The left half has mass per unit length µ= µ,12, while the right has a mass per unit length u' = 3µ = 3µ, / 2µ . Tension in the string is T. Notice from the data given that this string has the same total mass as a uniform string of length L and mass per unit length µ̟. (a) Find the speeds v and v' at which transverse pulses travel in the two sections. Express the speeds in terms of T, and u,, and also as multiples of the speed v, = (T,/ µ̟)"² . (b) Find the time interval required for a pulse to travel from one end of the string to the

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66. A string of length L consists of two sections. The left half has mass per unit length u= µ, /2, while the right has a mass per unit length µ' = 3µ = 3µ, 12µ. 0. Tension in the string is T. Notice from the data given that this string has the same total mass as a uniform string of length L and mass per unit length u. (a) Find the speeds v and v' at which transverse pulses travel in the two sections. Express the speeds in terms of T, and µ, and also as multiples of the speed v, = (T,I H)"². (b) Find the time interval required for a pulse to travel from one end of the string to the other. Give your result as a multiple of At = L/v,.
Transcribed Image Text:66. A string of length L consists of two sections. The left half has mass per unit length u= µ, /2, while the right has a mass per unit length µ' = 3µ = 3µ, 12µ. 0. Tension in the string is T. Notice from the data given that this string has the same total mass as a uniform string of length L and mass per unit length u. (a) Find the speeds v and v' at which transverse pulses travel in the two sections. Express the speeds in terms of T, and µ, and also as multiples of the speed v, = (T,I H)"². (b) Find the time interval required for a pulse to travel from one end of the string to the other. Give your result as a multiple of At = L/v,.
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