Since your associate's singing is not exactly music to your ears, you should meet with her to talk about it. Going to the source is an important step in this type of situation.
Obviously, you should not criticize her singing, even if it is causing the paint to peel off your walls. Rather, tell her that you need her help. Since she is a sweet and cheerful person, this should not be a great problem. Let her know that her singing is causing specific difficulties in your area, such as interfering with your concentration, interrupting phone calls, or making conversations more difficult. Politely ask her if there is a way she can help you by turning her volume way down.
If she either refuses to do so, or agrees and then makes no adjustment, then you should go back to your supervisor or office manager. Tell these individuals that your co-worker's behavior is interfering with productivity, performance, and, ironically, harmony in the department. By letting the department leaders see or hear the specific costs of your co-worker's behavior, they may start singing an entirely different tune.
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