11 grade physics others

A string is stretched between fixed points separated by 75.0 cm. It is observed to have resonant frequencies of 420Hz and 315Hz. There are no other resonant frequencies between these two. The lowest resonant frequency for this string is:

(a) 105Hz

(b) 155Hz

(c) 205Hz

(d) 10.5Hz

Aniket Singh

0 Years agoGrade

1 Answer

Askiitians Tutor Team

Approved Tutor Answer0 Years ago

To determine the lowest resonant frequency of the string, we can use the relationship between the frequencies of the harmonics. The given resonant frequencies are 420 Hz and 315 Hz. The difference between these two frequencies indicates that they are harmonics of the same fundamental frequency.

Finding the Fundamental Frequency

The frequencies can be expressed in terms of the fundamental frequency (f₁) and its harmonics:

f₁ = fundamental frequency
f₂ = 2 * f₁
f₃ = 3 * f₁

To find the fundamental frequency, we can calculate the greatest common divisor (GCD) of the two given frequencies:

Calculating the GCD

The GCD of 420 Hz and 315 Hz is 105 Hz. This means that the fundamental frequency of the string is:

f₁ = 105 Hz

Conclusion

Thus, the lowest resonant frequency for the string is (a) 105 Hz.