Exam 16: Superposition and Standing Waves

A vibrating tuning fork of 300 Hz is held above a tube filled with water.The first resonance is heard when the water level is lowered by 26.1 cm.A second tuning fork of 400 Hz is held above the tube,and its first resonance occurs when the water level is lowered by 19.3 cm from the top.Calculate a value for the speed of sound.(Hint: remember the small end correction $\Delta$ L at the top of the tube.)

A string fixed at both ends is vibrating in a standing wave.There are three nodes between the ends of the string,not including those on the ends.The string is vibrating at a frequency that is its

Which of the following equations represents a standing wave? (The symbols have their usual meaning.)

For a tube of length 57.0 cm that is open at both ends,what is the frequency of the fundamental mode? (the speed of sound in air is 340 m/s)

Four pendulums are hung from a light rod that is free to rotate about its long axis.The pendulums have lengths L,2L,L/2 and L,and masses m,m/2,2m and 4m respectively.Pendulum 1 is set to swing at its natural frequency.Which of the other three will,over time,also oscillate at the same frequency?

Two identical loudspeakers are driven in phase by the same amplifier.The speakers are positioned a distance of 3.2 m apart.A person stands 4.1 m away from one speaker and 4.8 m away from the other.Calculate the second lowest frequency that results in destructive interference at the point where the person is standing.Assume the speed of sound to be 340 m/s.

The wave function y(x,t)for a standing wave on a string fixed at both ends is given by y(x,t)= 0.080 sin 6.0x cos 600t where the units are SI.The distance between successive nodes on the string is