Question

An astronaut stretched a spring between two posts and measured the speed of a longitudinal wave on the spring. Which of the following would change the speed of a wave along the spring? More than one answer may be correct. Choose all that apply.

Stretching the spring a greater distance.

Using a spring with the same spring constant and same length but a different mass.

Using a spring with the same length and same mass but a different spring constant.

Keeping the same spring between the same posts but starting the wave with a greater amplitude.

Repeating the experiment on the moon.

Answer 1

Speed of wave on spring is given as

                      

where T is tension and is mass per unit length.

Stretching spring a greater distance will require increase in tension and hence speed increase.

Using a spring with the same spring constant and same length but a different mass will change mass per unit length and hence speed will change.

Using a spring with the same length and same mass but a different spring constant leads to different tension force and hence different speed.

Keeping the same spring between the same posts but starting the wave with a greater amplitude does not change the speed as speed does not depend on amplitude of wave.

Repeating experiment on moon will not change T or and hence speed will not change.