5. a. The frequency of a standing wave on a string is ƒ when the string's tension is Ts. If the tension is changed by the small amount ATs, without changing the length, show that the frequency changes by an amount Aƒ such that Af/f = (1/2)AT,/T,

The wave propagates at a speed of 12 m/s from A to B with the equation of "difference": y = 0.06 sin 20xt and the initial deviation is upwards (y and t are SI base units). The distance AB is 2.5 m. Exactly when B has 3/4 phase, point A deviates by... а. 3 ст, down b. 3 cm, up С. 3V3 ст, ир d. 3v3 cm, down е. б ст, down

Pr5. Two identical loudspeakers are located at points (-10,0,0) and (0,0, 10) of our coor- dinate system, where the numbers in the brac- kets correspond to the (r, y, z) coordinates of the points, expressed in meters. The loudspeakers are driven by the same oscillator with a frequ- ency of 170 Hz. The speed of sound in air can be considered 340 m/s. a) Give the coordinates of those points loca- ted on the positive r axis where the sound waves coming from the two loudspeakers interfere con- structively. b) A receiver is started to move slowly from the origin (0,0,0) along a path lying in the r-y plane so that it receives constant sound intensity throughout its slow motion. What is the shape of the path the receiver should take?

A string of mass 8 grams is stretched to a length of 0.3 meters and fastened at both end so that it can freely vibrate. The tension on the string is 1400 Newtons.   What is the linear density of the string? kg/m   At what speed would a wave propagate on this string? m/s   What is the wavelength of the first harmonic (also called the fundamental frequency) of standing wave created by the vibrating string? m   What is the fundamental frequency of the vibrating string? Hz