Question

A string vibrates in 5 segments to a frequency of 480 Hz. The frequency that will cause it to vibrate in 2 segments will be

Answer 1

When a string vibrates in 5 segment to a frequency of 480 Hz then we have ,
nλ/2 = L , where L is length of string and λ is wavelength of string
λ = 2L/n and frequency = v/λ = nv/2L , here v is speed of wave.

∴ frequency of 480 Hz is given by , 480 Hz = 5v/2L -----(1)
In 2nd segment , frequency , f = 2v/L -----(2)

Dividing equation (2) from (1),
f/480 = 2/5
⇒ f/480 = 2/5
⇒ f = 480 × 2/5 = 96 × 2 = 192 Hz

Hence, frequency = 192 Hz

Answer 2

Hello Dear.

Here is the answer----


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Given,

In First Case,

   Number of Segments(n)  = 5 Segments.
 Frequency of Sound produced by them(f) = 480 Hz.

Using the Formula,

     Length of the String(L) = nλ/2
                                       L   = [n(v/f)] ÷ 2 [Since λ = v/f]
                                  ⇒    f   = nv/2L   -----------------eq(i)
    
Where, v = Speed of the Sound Wave.
             f = Frequency of the wave.
            λ = Wavelength of the Wave.



  Thus, 480 = 5v/2L        ------------------------------eq(ii)

In Second Case,

    f₁ = ?
  n₁ = 2 segments

Thus, Using the Relation of eq(i),

We get,

      f₁ = 2v/L  ----------------------------eq(iii)

Dividing eq(ii) by eq(iii),

 We get,  
    480/f₁ = (5v/2L) ÷ (2v/L)

⇒   480/f₁  =  5/4
⇒    f₁ =  (480 × 4) ÷ 5
⇒    f₁ = 384 Hz


Thus, the Frequency of the sound wave as produced by the 2 segments of the strings is 384 Hz.

      
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Hope it helps.


Have a Marvelous Day.