Opening holes in the side effectively shortens the length of the resonant column. If the highest note a piccolo can sound is 39.4 kHz, find the distance between adjacent antinodes for this mode of vibration. Assume the speed of sound is 343 m/s.

Two identical piano wires have a fundamental frequency of 555 Hz when kept under the same tension. What fractional increase in the tension of one wire will lead to the occurrence of 7 beats/s when both wires oscillate simultaneously?

(a) Expectant parents are thrilled to hear their unborn baby's heartbeat, revealed by an ultrasonic motion detector. Suppose the fetus's ventricular wall moves in simple harmonic motion with an amplitude of 1.70mm and a frequency of 130. per minute. Calculate the maximum linear speed of the heart wall. Suppose the motion detector in contact with the mother's abdomen produces sound at 1910000Hz, which travels through tissue at 1.50km/s. (b) Calculate the maximum frequency at which the sound would be perceived at the wall of the baby's heart. (c) Calculate the maximum frequency at which reflected sound is received by the motion detector. (By electronically "listening" for echoes at a frequency different from the broadcast frequency, the motion detector can produce beeps of audible sound in synchronization with the fetal heartbeat.)

A stretched string fixed at each end has a mass of 37.0 g and a length of 9.00 m. The tension in the string is 44.0 N. (a) Determine the positions of the nodes and antinodes for the third harmonic. (Enter your answers from smallest to largest distance from one end of the string.)nodes:  ?m ? m  ? m ? m antinodes: ? m  ?m  ?m (b) What is the vibration frequency for this harmonic? ?Hz