# physics

posted by .

A stretched wire vibrates in its fundamental mode at a frequency of 420 Hz. What would be the fundamental frequency if the wire were one fourth as long, its diameter were quadrupled, and its tension were increased two-fold?

• physics -

With 4 times the diameter (and assuming the same material density), the mass per unit length would increase by a factor of 16. The ratio (tension)/(linear density) would be 2/16 = 1/8 of its previous value. The wave speed is proportional to the square root of that, or 0.3536 as large as before.

The fundamental frequency is proportional to (wave speed)/(length). This changes by a factor 0.3536/0.250 = 1.414

The new fundamential frequency is 594 Hz.

## Similar Questions

A 38 cm length of wire has a mass of 6.0 g. It is stretched between two fixed supports and is under a tension of 145 N. What is the fundamental frequency of this wire?
2. ### Physics Help!!!

One of the 79.0 -long strings of an ordinary guitar is tuned to produce the note (frequency 245 ) when vibrating in its fundamental mode. Part A- If the tension in this string is increased by 3.2 , what will be the new fundamental …
3. ### Physics Help!!!

One of the 79.0 -long strings of an ordinary guitar is tuned to produce the note (frequency 245 ) when vibrating in its fundamental mode. Part A- If the tension in this string is increased by 3.2 , what will be the new fundamental …
4. ### physics

A large rock that weighs 164.0 N is suspended from the lower end of a thin wire that is 3.00 m long. The density of the rock is 3200 kg/m^3. The mass of the wire is small enough that its effect on the tension in the wire can be neglected. …
5. ### physics

a wire under tension vibrates with a fundamental frequency of 256Hz. what would be the fundamental frequency if the wire were half as long, twice as thick, and under 1/4 tension?
6. ### physics

steeel and silver wire of the same diameter and same length are stretched with equal tension. what is the fundamental frequency of the silver wire if that of the steel is 200 Hz.
7. ### Physics, waves

A string vibrates in its fundamental mode with a frequency of 200 Hz. The string is 0.64 m long and has a mass of 1.61 g. With what tension must the string be stretched?
8. ### Physics

A stretched wire 75cm long emits a fundamental frequency of 300Hz.By how much the length be changed so that it emits a fundamental note of 450Hz?
9. ### Physics

A large rock that weighs 164.0 N is suspended from the lower end of a thin wire that is 3.00 m long. The density of the rock is 3200 kg/m3. The mass of the wire is small enough that its effect on the tension in the wire can be neglected. …
10. ### Physics

A string of length L vibrates with a fundamental frequency f when under a tension of 100 N. What is the fundamental frequency of the string when its tension is increased to 2500 N?

More Similar Questions