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A point mass M is suspended in the middle of a string whose ends are fixed...

A point mass M is suspended in the middle of a string whose ends are fixed at the same level distance 2ℓ apart; the mass is distance h below the ends of the string. The total mass of the string is m ≪ M. (a) Find the speed of sound waves along the string and (b) the principal frequency of string vibrations on either side of the mass. (c) Do you think this is the smallest vibration frequency in the system? If not, describe the vibration mode and calculate the corresponding frequency

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