A sonometer wire of length 80 cm and a tuning fork sounded together produces 5 beats per second. The same number of beats per second is produced when the length of the wire is increased to 85 cm . What is the frequency of the tuning fork?

Step-by-step solution

Let f be the frequency of the tuning fork and f₁, f₂ be the frequencies of the sonometer wire at lengths l₁ = 80 cm and l₂ = 85 cm respectively. The frequency of a sonometer wire is given by f = 1 2l T , which implies f 1 l . Thus, f₁ l₁ = f₂ l₂ = k , where k is a constant. Given that the wire produces 5 beats per second with the tuning fork in both cases, we have |f - f₁| = 5 and |f - f₂| = 5 . Since l₂ > l₁ , it follows that f₂ Using the relation f₁ l₁ = f₂ l₂ , we substitute the values: (f + 5) 80 = (f - 5) 85 D