Apiano tuner stretches a steel piano wire with a tension of 1070 n . the wire is 0.400 m long and has a mass of 4.00 g . a. what is the frequency of its fundamental mode of vibration?
b. what is the number of the highest harmonic that could be heard by a person who is capable of hearing frequencies up to 1.00×10^4 hz ?

A. 409 Hz

The fundamental frequency of a string is given by:

where

L is the length of the wire

T is the tension in the wire

m is the mass of the wire

For the piano wire in this problem,

L = 0.400 m

T = 1070 N

m = 4.00 g = 0.004 kg

So the fundamental frequency is

B. 24

For this part, we need to analyze the different harmonics of the piano wire. The nth-harmonic of a string is given by

where is the fundamental frequency.

Here in this case

A person is capable to hear frequencies up to

So the highest harmonics that can be heard by a human can be found as follows:

most voltage drop calculators want the distance between the source and destination. then internally, they double it so both the source and return wires are calculated. but you need to know which distance the calculator uses so you're not half of what you should be or double what you should be.

most circuit breakers will not take a #6 directly, so the electrician will have to splice on a smaller pigtail. you also have to upsize the grounding wire when you upsized the ungrounded (hot) wire (see note in 250.122). this will preclude using most cable assemblies, as a cable with #6 copper will most likely only have a #10 grounding conductor. you need a #6 grounding conductor if the circuit is 20a. a #8 cable is no better, as it will have a #10 grounding conductor too. but most 20a breakers will take a #8 directly.

in your related post, you didn't say what type of load this is. if it is a light or heater, voltage drop won't be a big issue. if this is a motor, the current needs are huge at startup and the voltage drop can pose a problem. if this is a motor, knowing if the motor is under much load during startup will answer the voltage drop effect (a saw is easier to start than a compressor).

the answer would be c