Question

A rope with a linear mass density of 64 g/m is held under tension of 6 N. A student moves one end of the rope up and down, creating a wave on the rope.

If the end of the rope is attached to a thicker rope, with a linear mass density of 182 g/m, what must the frequency of the wave be in the thicker rope? The student moves the thin rope up and down 6 times per second. The frequency of the wave in the thicker rope is ______Hz.

Speed of wave on original rope: 9.682458366 m/s

Wavelength of original wave: 3.227486122 m

To be Clear: THE ANSWER IS NOT 0.1667 HZ

Answer 1

Frequency is the basic characteristic of waves. When wave propagates from thin rope to thick rope the frequency remains the same , it is because making the wave continuous. If frequencies are not same wave cannot transmit into second rope. It is like the ray of light is entering from air to water, the frequency remains the same but wavelength and velocity of wave changes according to the refractive index of the water.

Same here, the wavelength and velocity of wave will be changed according to the density of second rope (as tension rremains same) and frequency remains same.

So, frequency of wave in thicker rope is 6 Hz.