a sonometer wire has  a length 114 cm between two fixeed ends.where should be two bridges placed so that 3 segments have fundamental frequencies in the ratio 1:3:4?

Fundamental wavelength of a wave travelling on the string of length l is given as l = λ/2. As the frequency of the wave is inversely proportional to the wavelength for a constant velocity, ratio of wavelengths will be 1 : (1/3) : (1/4)

or 12 : 4 : 3

You can write 12k + 4k + 3k = 114 cm, where k is the common factor. (because, lengths are directly proportional to the wavelength)

⇒ k = 6

Hence, length of the strings are, 72 cm, 24 cm and 18 cm.

Thus, from the left end the bridges should be placed at 72 cm and 96 cm (72 + 24)

Remember, considering distance from right end distances will be changed.

 

Hope it is clear!

Best wishes!!