Will increasing the energy of a string increase the velocity

[HHH]

Homework Statement

In a test, I was told to identify 3 characteristics that could increase the velocity of the sound traveling through a cup and wire phone. This was a sound and waves unit test.

Homework Equations

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The Attempt at a Solution

I wrote that the linear density could be decreased, the force of tension in the string could be increased and that the cups and wire themselves could be of the same resonant frequency.

My first two reasons are from the equation Velocity = √((Force of Tension)/(linear density)). The third reasoning was based on the idea that if they are of the same resonant frequency, less energy would be lost going from medium to medium. I said that because there is more energy in the string, the velocity would increase.

The teacher agreed that there would be more energy, but said that more energy in the string would only result in a greater amplitude. I had thought that more energy == greater velocity? Is that assumption incorrect then?

Thanks for any help.

 

[NascentOxygen]

It's a good idea to minimize losses, but a more energetic vibration doesn't mean it travels faster. (If you want to convince otherwise, you'd need to come up with equations that support that contention.)

If an axeman brings the axe down more forcefully, the sound doesn't travel through the air to reach a distant listener noticeably any faster than when he chops less energetically.

Did you find out what the third change was, to increase speed?

I remember as a kid making these tin can phones, and we waxed the string, using a lump of beeswax. I'm now wondering what that achieved.