Question

A standing wave is set up in a 200-cm string fixed at both ends. The string vibrates in 5 distinct segments when driven by a 120-Hz source. What is the wavelength of the standing wave?

1) 10 cm
2) 20 cm
3) 40 cm
4) 80 cm
5) 100 cm

Answer 1

The wavelength of the standing wave set up in a 200-cm string fixed at both ends, vibrating in 5 segments, is 80 cm.

Step-by-step explanation:

The question refers to a standing wave in a string that is fixed at both ends and divided into 5 distinct segments by the standing wave pattern. These segments are created by nodes and antinodes. For a string fixed at both ends, the length of the string is equal to half a wavelength times the number of segments. Since the string vibrates in 5 segments, it has 4 nodes (excluding the fixed ends), which means there are 4.5 wavelengths within the 200-cm string. Therefore, the length of one wavelength (lambda) can be calculated by dividing the total length of the string by the number of half-wavelengths:

• Total length of string (L) = 200 cm
• Number of half-wavelengths (n) = 5
• Wavelength (lambda) = 2L/n = 2 × 200 cm / 5 = 80 cm

In summary, the wavelength of the standing wave set up in the 200-cm string is 80 cm.