Question

question 11 (1 point)
if a guitar string has a fundamental frequency of 500 hz, which one of the following frequencies
can set the string into resonant vibration?

a) 1750 hz

b) 1250 hz

c) 1500 hz

d) 250 hz

e) 750 hz

Explanation:

Step1: Recall Resonance in Strings

A guitar string (fixed at both ends) vibrates at fundamental frequency \( f_1 \) and its harmonics \( f_n = nf_1 \), where \( n = 1, 2, 3, \dots \). Resonance occurs at these harmonic frequencies.

Step2: Check Each Option

• Option a: \( 1750 \div 500 = 3.5 \) (not an integer, so not a harmonic).
• Option b: \( 1250 \div 500 = 2.5 \) (not an integer, so not a harmonic).
• Option c: \( 1500 \div 500 = 3 \) (integer, so \( n = 3 \), a harmonic).
• Option d: \( 250 \div 500 = 0.5 \) (not an integer, lower than fundamental, no resonance).
• Option e: \( 750 \div 500 = 1.5 \) (not an integer, so not a harmonic).

Answer:

c) 1500 Hz