Tag: standing waves in strings

Questions Related to standing waves in strings

The second overtone of an open pipe has the same frequency as the first overtone of a closed pipe 2 m long. The length of the open pipe is

physics oscillations and waves standing waves in strings standing waves reflection of waves

  1. 8 m

  2. 4 m

  3. 2 m

  4. 1 m

Show answer
Correct Option: B
Explanation:

$l _0=$ length of organ pipe (open)

$l _c=$ length of close organ pipe
frequency of open pipe$=\cfrac{3V}{2l _0}$
frequency of close pipe $=\cfrac{3V}{2l _c}$
$\therefore \cfrac{3V}{2l _0}=\cfrac{3V}{4l _c}\2l _0=4l _c\2\times2m=4m$
B is the correct option.

A guitar string is $90 cm$ long and has a fundamental frequency of $124 Hz$. To produce a fundamental frequency of $186 Hz$, the guitar should be pressed at ?

physics oscillations and waves standing waves in strings standing waves reflection of waves

  1. $60 cm$

  2. $30 cm$

  3. $20 cm$

  4. $ 10 cm$

Show answer
Correct Option: A
Explanation:

Here, $L _1 = 90 cm, \upsilon _1 = 124 Hz, \upsilon _2 = 186 Hz, L _2=?$

According to the law of length, $\upsilon _2L _2 = \upsilon _1L _1$

$\therefore \upsilon _2= \dfrac{\upsilon _1L _1}{\upsilon _2} = \dfrac{124 \times 90}{186} = 60 cm$