Question

In each case indicate whether the quantity in question increased, decreased or stayed the same when the string length is increased. Assume that the tension is unchanged. The function generator is kept at the same frequency, and the string is in resonance in all cases. Part A Number of antinodes ___ Number of antinodes ___ increased. decreased. stayed the same. Request Answer Part B Wavelength ___ Wavelength ___ increased. decreased. stayed the same. Request Answer Part C Fundamental frequency ___ Fundamental frequency ___ increased. decreased. stayed the same.

Answer 1

Answer:

Answer: No of anti-nodes increases

Answer: wavelength remains same.

Answer: fundamental frequency decreases

Explanation:

a)

The number of nodes (n) would have (n-1) anti-nodes.

The relation of Length of string with n is given below:

$L = \frac{n*lambda}{2}$

Hence, n and L are directly proportional so as string length increases number of nodes and anti-nodes also increases.

Answer: No of anti-nodes increases

b)

Wavelength is dependent on the frequency:

$lambda = \frac{v}{f}$

The speed v of the string remains same through-out and frequency of generator is unchanged!

Hence according to above relationship lambda is unchanged.

Answer: wavelength remains same.

C

Fundamental frequency equates to 1st harmonic that 2 nodes and 1 anti-node. Wavelength is = 2*L

Hence, if L increases wavelength increases

Using relation in part b

As wavelength increases fundamental frequency decreases

Answer: fundamental frequency decreases