physics

posted by .

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?

  • physics -

    The speed of transverse waves is the squareroot of (T/p), where p is the density per unit length, and T is the tension foorce. The density per unit length is 4x higher for the shorter, fatter wire, and T is 1/4 as high, to the sound speed is 1/4 as large.

    The wavelength of the fundamental is 1/2 as long due to the shorter length.

    The fundamental frequency scales with (sound speed)/(wavelength), and gets multiplied by (1/4)/(1/2) = 1/2

  • Physics -

    f1=v1/L1=(1/L1)(T1/μ1)^1/2
    f2=v2/L2=(1/L2)(T2/μ2)^1/2
    then
    f2/f1=(L1/L2)[T2μ1/(T1μ2)]^1/2
    where
    L2=1/2L1
    T2=1/4T1
    μ2=ρS2=4ρS1=4μ1
    then
    f2=1/2f1
    f2=128 hz

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. physics

    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?
  2. Physics

    The transverse standing wave on a string fixed at both ends is vibrating at its fundamental frequency of 250 Hz. What would be the fundamental frequency on a piece of the same string that is twice as long and has four times the tension?
  3. Physics

    The transverse standing wave on a string fixed at both ends is vibrating at its fundamental frequency of 250 Hz. What would be the fundamental frequency on a piece of the same string that is twice as long and has four times the tension?
  4. Physics - PLease Help!

    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?
  5. 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. …
  6. Physics

    A 48-cm-long wire with a mass of 11.0 g is under a tension of 50.5 N. Both ends of the wire are held rigidly while it is plucked. (a) What is the speed of the waves on the wire?
  7. physics

    A solid copper object hangs at the bottom of a steel wire of negligible mass. The top end of the wire is fixed. When the wire is struck, it emits a sound with a fundamental frequency of 135 Hz. The copper object is then submerged in …
  8. 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. …
  9. 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?
  10. physics

    Where F is the tension in the string and ยต is the linear density (mass per length) of the string. A violin string vibrates at the fundamental frequency of 512 Hz under the tension of 480 N. What should be the tension in the string …

More Similar Questions