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The velocity v of a transverse wave on a stretched string is given by v = sqrt(T/u). Identify the terms T and u, and show that the equation is dimensionally correct. Write down an expression for the frequency of the nth overtone of a vibrating wire of fundamental frequency f. Why does the note sounded by a vibrating sonometer wire sound different when it is plucked in the middle from when it is plucked near one end?

The velocity v of a transverse wave on a stretched string is given by v = sqrt(T/u). Identify the terms T and u, and show that the equation is dimensionally correct. Write down an expression for the frequency of the nth overtone of a vibrating wire of fundamental frequency f. Why does the note sounded by a vibrating sonometer wire sound different when it is plucked in the middle from when it is plucked near one end?

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The velocity v of a transverse wave on a stretched string is given by v = sqrt(T/u).

  • Identify the terms T and u, and show that the equation is dimensionally correct.
  • Write down an expression for the frequency of the nth overtone of a vibrating wire of fundamental frequency f.
  • Why does the note sounded by a vibrating sonometer wire sound different when it is plucked in the middle from when it is plucked near one end? 
Exercise 2 The velocity v of a transverse wave on a stretched string is given by v = (a.) Identify the terms T and u, and hence show that the equation is dimensionally correct. (b.) (i.) Derive an expression for the fundamental frequency of a vibrating wire. (ii.) Describe how you would use a sonometer wire to determine experimentally how the fundamental frequency of a vibrating wire depends upon one of the variables in the expression in b (i) above. (c.) (i.) Write down an expression for the frequency of the n" overtone of a vibrating wire of fundamental frequency f. (ii.) Why does the note sounded by a vibrating sonometer wire sound different when it is plucked in the middle from when it is plucked near one end?
Transcribed Image Text:Exercise 2 The velocity v of a transverse wave on a stretched string is given by v = (a.) Identify the terms T and u, and hence show that the equation is dimensionally correct. (b.) (i.) Derive an expression for the fundamental frequency of a vibrating wire. (ii.) Describe how you would use a sonometer wire to determine experimentally how the fundamental frequency of a vibrating wire depends upon one of the variables in the expression in b (i) above. (c.) (i.) Write down an expression for the frequency of the n" overtone of a vibrating wire of fundamental frequency f. (ii.) Why does the note sounded by a vibrating sonometer wire sound different when it is plucked in the middle from when it is plucked near one end?
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