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. Request Answer Part D Fundamental wavelength ___ Fundamental wavelength ___ increased. decreased. stayed the same. Request Answer Part E Wave speed ___ Wave speed ___ increased. decreased. stayed the same.

Answer 1

Answer:

a) the number of antinodes increases , b) wavelength produced is constant.

, c) fundamental frequency is constant., d)  fundamental wavelength does not change, e)  the speed of the wave is constant

Explanation:

This is a resonance problem where we have a frequency generator, attached to a chain with a weight in its final part, at the two ends there is a node, point if movement. The condition for resonance of this system is

         λ = 2 L / n

  Where n is an integer

         L = n λ / 2

Let's review the problem questions.

A) As the length of the chain increases the number of wavelengths (Lam / 2) should increase, so the number of antinodes increases

B) when seeing the first equation the wavelength remains the same since the change in the length of the chain and the change in the number between are compensated, therefore for a configuration of generator frequency and weight applied the wavelength produced is constant.

C) the speed of the wave is

         v = λ f

In a string the speed is constant for a fixed applied weight, with the wavelength we did not change, therefore the fundamental frequency must also be constant.

D) The value of the fundamental wavelength does not change if the weight does not change, but there is a minimum chain length for this resonance to be observed and corresponds to n = 1

              L = λ / 2

E) the speed of the wave depends on the chain tension and its density if they do not change the speed of the wave does not change either